Putting in expressions for Z(out) & Z(cap) as obtained in (2) & (3) into (4) we get

Z(tot) = 1/sC + sLR/{R + sL}

Z(tot) = ({R + sL} + (s^2)*LCR)/sC(R + sL) (5)

Now by the voltage divider rule we can say that the transfer function
Av = V(out)/V(in) = Z(out)/Z(tot) (6)

Av = Z(out)/{Z(tot)} (7)

Av = sLR/{R + sL}*sC(R + sL)/({R + sL} + s^2*LCR)

Av = sLR*sC*(R + sL)/(R +sL)*({R + sL} + s^2*LCR) (8)

Reducing to

Av = s^2*LCR/({R + sL} + s^2LCR) ...

Solution Summary

An LCR circuit is presented and the transfer function of Vout/Vin is determined based on known passive values. An expression for the phase is determined and questions about zero phase are asked and answered. The Thevenin equivalent circuit is deduced and the Thevenin emf and input impedance worked out